The fragment separator of the Facility for Rare Isotope Beams uses six warm iron large acceptance high field superconducting quadrupole magnets (see <xref ref-type="fig" rid="fig1">Fig. 1</xref>). These magnets are located underground in the target facility hot cell. This location does not allow liquid nitrogen to be used for the cooling of the thermal shield so 35-K helium gas is used instead. In the event of a quench, the decaying field in the magnet induces eddy currents that give rise to a large force on the thermal shields. Because of the multifaceted geometry of the shield, understanding this force is an important aspect of the design. Detailed eddy current simulations were performed and the forces on the different parts of the shield were studied by finite-element analysis. This paper presents the results obtained for the stress distribution, the deformation in the thermal shield, and also mechanical design details.